IntroductionIntroduction toto PHYSICALPHYSICAL OCEANOGRAPHYOCEANOGRAPHY RobertRobert H StewartStewart Chapter 3 The Physical Setting Earth is an oblate ellipsoid, an ellipse rotated about its minor axis, with an equatorial radius of Re =6, 378.1349 km (West, 1982) slightly greater than the polar radius of Rp =6, 356.7497 km. The small equatorial bulge is due to earth’s rotation. Distances on earth are measured in many different units, the most common are degrees of latitude or longitude, meters, miles, and nautical miles. Latitude is the angle between the local vertical and the equatorial plane. A meridian is the intersection at earth’s surface of a plane perpendicular to the equatorial plane and passing through earth’s axis of rotation. Longitude is the angle between the standard meridian and any other meridian, where the standard meridian is the one that passes through a point at the Royal Observatory atGreenwich, England. Thus longitude is measured east or west of Greenwich. Adegreeoflatitudeisnotthesamelengthasadegreeoflongitude except at the equator. Latitude is measured along great circles withradiusR,where R is the mean radius of earth. Longitude is measured along circles with radius R cos ϕ,whereϕ is latitude. Thus 1◦ latitude = 111 km, and 1◦ longitude =111cosϕ km. Because distance in degrees of longitude is not constant, oceanographers measure distance on maps using degrees of latitude. Nautical miles and meters are connected historically to the size of earth. Gabriel Mouton proposed in 1670 a decimal system of measurement based on the length of an arc that is one minute of a great circle of earth. This eventually became the nautical mile. Mouton’s decimal system eventually became the metric system based on a different unit of length, the meter, which was originally intended to be one ten-millionth the distance from the Equator to the pole along the Paris meridian. Although the tie between nautical miles,meters,andearth’s radius was soon abandoned because it was not practical, the approximations are very good. For example, earth’s polar circumference is approximately 40,008 km. Therefore one ten-millionth of a quadrant is 1.0002 m. Similarly, a nautical mile should be 1.8522 km, which is very close to the official definition of the international nautical mile:1nm 1.8520 km. ≡ 21 22 CHAPTER 3. THE PHYSICAL SETTING 90 o 60 o 30 o 0 0 -30 0 -60 o -90 o -80 o -40 o 0 o 40 o -4000 -3000 -1000 -200 0 Figure 3.1 The Atlantic Ocean viewed with an Eckert VI equal-area projection. Depths, in meters, are from the etopo 30′ data set. The 200 m contour outlines continental shelves. 3.1 Ocean and Seas There is only one ocean. It is divided into three named parts byinternational agreement: the Atlantic, Pacific, and Indian ocean (International Hydrographic Bureau, 1953). Seas, which are part of the ocean, are defined inseveralways.I consider two. The Atlantic Ocean extends northward from Antarctica and includes all of the Arctic Sea, the European Mediterranean, and the American Mediter- ranean more commonly known as the Caribbean sea (figure 3.1). The boundary between the Atlantic and Indian Ocean is the meridian of Cape Agulhas (20◦E). The boundary between the Atlantic and Pacific is the line forming the short- est distance from Cape Horn to the South Shetland Islands. In the north, the Arctic Sea is part of the Atlantic Ocean, and the Bering Straitistheboundary between the Atlantic and Pacific. The Pacific Ocean extends northward from Antarctica to the Bering Strait (figure 3.2). The boundary between the Pacific and Indian Oceanfollowsthe 3.2. DIMENSIONS OF THE OCEAN 23 90 o 60 o 30 o 0 o -30 o -60 o -90 o 120o 160 o -160 o -120 o -80o -4000 -3000 -1000 -200 0 Figure 3.2 The Pacific Ocean viewed with an Eckert VI equal-area projection. Depths, in meters, are from the etopo 30′ data set. The 200 m contour outlines continental shelves. line from the Malay Peninsula through Sumatra, Java, Timor, Australia at Cape Londonderry, and Tasmania. From Tasmania to Antarctica it isthemeridian of South East Cape on Tasmania 147◦E. The Indian Ocean extends from Antarctica to the continent of Asia in- cluding the Red Sea and Persian Gulf (figure 3.3). Some authorsusethename Southern Ocean to describe the ocean surrounding Antarctica. Mediterranean Seas are mostly surrounded by land. By this definition, the Arctic and Caribbean Seas are both Mediterranean Seas, the Arctic Mediter- ranean and the Caribbean Mediterranean. Marginal Seas are defined by only an indentation in the coast. The Arabian Sea and South China Sea are marginal seas. 3.2 Dimensions of the ocean The ocean and seas cover 70.8% of the surface of earth, which amounts to 361,254,000 km2.Theareasofthenamedpartsvaryconsiderably(table3.1). 24 CHAPTER 3. THE PHYSICAL SETTING 30 o 0 o -30 o -60 o -90 o 40 o 80 o 120 o -4000 -3000 -1000 -200 0 Figure 3.3 The Indian Ocean viewed with an Eckert VI equal-area projection. Depths, in meters, are from the etopo 30′ data set. The 200 m contour outlines continental shelves. Oceanic dimensions range from around 1500 km for the minimum width of the Atlantic to more than 13,000 km for the north-south extentoftheAtlantic and the width of the Pacific. Typical depths are only 3–4 km. So horizontal dimensions of ocean basins are 1,000 times greater than the vertical dimension. AscalemodelofthePacific,thesizeofan8.5 11 in sheet of paper, would have dimensions similar to the paper: a width of× 10,000 km scales to 10 in, and adepthof3kmscalesto0.003in,thetypicalthicknessofapiece of paper. Because the ocean is so thin, cross-sectional plots of ocean basins must have a greatly exaggerated vertical scale to be useful. Typical plots have a vertical scale that is 200 times the horizontal scale (figure 3.4). This exaggeration distorts our view of the ocean. The edges of the ocean basins, the continental slopes, are not steep cliffs as shown in the figure at 41◦Wand12◦E. Rather, they are gentle slopes dropping down 1 meter for every 20 meters in the horizontal. The small ratio of depth to width of the ocean basins is very important for understanding ocean currents. Vertical velocities mustbemuchsmaller Table 3.1 Surface Area of the ocean † Pacific Ocean 181.34 × 106 km2 Atlantic Ocean 106.57 × 106 km2 Indian Ocean 74.12 × 106 km2 † From Menard and Smith (1966) 3.3. SEA-FLOOR FEATURES 25 0 -2 Depth (km) -4 -6 -45 o -30 o -15 o 0 o 15 o Longitude 6 km 6 km -45 o -30 o -15 o 0 o 15 o Figure 3.4 Cross-section of the south Atlantic along 25◦Sshowingthecontinentalshelf offshore of South America, a seamount near 35◦W, the mid-Atlantic Ridge near 14◦W, the Walvis Ridge near 6◦E, and the narrow continental shelf offSouth Africa. Upper Vertical exaggeration of 180:1. Lower Vertical exaggeration of 30:1. If shown with true aspect ratio, the plot would be the thickness of the line at the sea surface inthelowerplot. than horizontal velocities. Even over distances of a few hundred kilometers, the vertical velocity must be less than 1% of the horizontal velocity. I will use this information later to simplify the equations of motion. The relatively small vertical velocities have great influence on turbulence. Three dimensional turbulence is fundamentally different than two-dimensional turbulence. In two dimensions, vortex lines must always be vertical, and there can be little vortex stretching. In three dimensions, vortexstretchingplaysa fundamental role in turbulence. 3.3 Sea-Floor Features Earth’s rocky surface is divided into two types: oceanic, with a thin dense crust about 10 km thick, and continental, with a thick light crust about 40 km thick. The deep, lighter continental crust floats higher on the denser mantle than does the oceanic crust, and the mean height of the crust relative to sea level has two distinct values: continents have a mean elevation of 1100 m, the ocean has a mean depth of -3400 m (figure 3.5). The volume of the water in the ocean exceeds the volume of the ocean basins, and some water spills over on to the low lying areas of the continents. These shallow seas are the continental shelves. Some, such as the South China Sea, are more than 1100 km wide. Most are relatively shallow, with typical depths of 50–100 m. A few of the more important shelves are: the East China Sea, the Bering Sea, the North Sea, the Grand Banks, the Patagonian Shelf, the Arafura Sea and Gulf of Carpentaria, and the Siberian Shelf. The shallow seas help dissipate tides, they are often areas of high biological productivity, and they are usually included in the exclusive economic zone of adjacent countries. 26 CHAPTER 3. THE PHYSICAL SETTING Frequency (% Area) 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00% 10,000 8,000 6,000 4,000 2,000 meters) n ( 0 tio -2,000 Eleva -4,000 -6,000 -8,000 -10,000 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Cumulative (% Area) Figure 3.5 Histogram of height of land and depth of the sea as percentage of area of earth in 100 m intervals, showing the clear distinction between continents and sea floor. The cumulative frequency curve is the integral of the histogram.Thecurvesarecalculatedfrom the etopo 2datasetbyGeorgeSharmanofthenoaa National Geophysical Data Center. The crust is broken into large plates that move relative to each other.